Multivariate process variability monitoring for high dimensional data

In today’s competitive market, the quality of a product or service is no longer measured by a single variable but by a number of variables that define the quality of the final product or service. It is known that these quality variables of products or services are correlated with each other, and it is therefore important to monitor these correlated quality characteristics simultaneously. Multivariate quality control charts are capable of such monitoring. Multivariate monitoring of industrial or clinical procedures often involves more than three correlated quality characteristics, and the status of the process is judged using a sample of one size. The majority of existing control charts for monitoring multivariate process variability for individual observations are capable of monitoring up to three quality characteristics. One of the hurdles in designing optimal variability control charts for large dimension data is the enormous computing resources and time that is required by the simulation algorithm to estimate the charts parameters. In this research, a novel algorithm based on the parallelised Monte Carlo simulation has been developed to improve the ability of the Multivariate Exponentially Weighted Mean Squared Deviation (MEWMS) and Multivariate Exponentially Weighted Moving Variance (MEWMV) charts to monitor multivariate process variability with a greater number of quality characteristics. Different techniques have been deployed to reduce computing space and the time complexity taken by the algorithm. The novelty of this algorithm is its ability to estimate the optimal control limit L (optimal L) for any given number of correlated quality characteristics, size of the shifts to be detected based on the smoothing constant, and the given in-control average run length in a computationally efficient way. The optimal L for the MEWMS and MEWMV charts to detect small, medium and large shifts in the covariance matrix of up to fifteen correlated quality characteristics has been provided. Furthermore, utilising the large number of optimal L values generated by the algorithm has enabled us to develop two mathematical functions that are capable of predicting L values for MEWMS and MEWMV charts. This would eliminate the need for further execution of the parallelised Monte Carlo simulation for high dimension data. One of the main challenges in deploying multivariate control charts is to identify which characteristics are responsible for the out-of-control signal detected by the charts, and what is the extent of their contribution to the signal. In this research, a smart diagnostic technique has been developed by using a hybrid of the wrapper filter approach to effectively identify the variables that are responsible for the process faults and to classify the percentage of their contribution to the faults. The robustness of the proposed techniques has been demonstrated through their application to a range of clinical and industrial multivariate processes where the percentage of correct classifications is presented for different scenarios. The majority of the existing multivariate control charts have been developed to monitor processes that follow multivariate normal distribution. In this thesis, the author has proposed a control chart for a non-normal high dimensional multivariate process based on the percentile point of Burr XII distribution. Geometric distance variables are fitted to the subset of correlated quality characteristics to reduce the dimension of the data, which is then followed by fitting the Burr XII distribution to each geometric distance variable. Since individual distance variables are independent, each can be monitored by individual control charts based on the percentile points of the fitted Burr XII distributions. A simulated annealing approach is used to estimate parameters of the Burr XII distribution. The proposed hybrid is utilised to identify and rank the variables responsible for the out-of-control signals of geometric distance variables